ABSTRACT
Consider the problem of r t / randomly distributed points in a unit n-ball and the convex hull created by these points. Let ~ 11 be r.t times the r-content of an rsimplex whose p vertices are in the interior and r + /- p vertices on the boundary of a unit n-ball. Explicit expressions for the exact distribution functions of ~,, are given when r 1 / points are independently, and identically distributed according to the Uniform distribution. The exact distributions are obtained using the technique · of Inverse Mellin transforms with the help of the moment functions. The technique is illustrated for the general case p =- r -1 1 and a particular case p =3, r -2 . Various representations of the distributions in psi and the generalized zeta functions are given. These representations are also given in the most general case as an H-function distribution.
KENNEDY, O (2021). Finding The Distribution Of A Random Variable From Its Moment Function. Afribary. Retrieved from https://afribary.com/works/finding-the-distribution-of-a-random-variable-from-its-moment-function
KENNEDY, OTWOMBE "Finding The Distribution Of A Random Variable From Its Moment Function" Afribary. Afribary, 28 May. 2021, https://afribary.com/works/finding-the-distribution-of-a-random-variable-from-its-moment-function. Accessed 26 Apr. 2024.
KENNEDY, OTWOMBE . "Finding The Distribution Of A Random Variable From Its Moment Function". Afribary, Afribary, 28 May. 2021. Web. 26 Apr. 2024. < https://afribary.com/works/finding-the-distribution-of-a-random-variable-from-its-moment-function >.
KENNEDY, OTWOMBE . "Finding The Distribution Of A Random Variable From Its Moment Function" Afribary (2021). Accessed April 26, 2024. https://afribary.com/works/finding-the-distribution-of-a-random-variable-from-its-moment-function